Problem: David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is $15:1$. He currently has $40$ grams of the spice blend, and he can go buy more if necessary. He wants to make $10$ servings, where each serving has $75$ grams of rice. Overall, David spends $4.50$ dollars on rice. What is the price of rice per gram?
Answer: There can be many ways to solve this problem. Here, we will do this by thinking about units. Let's say the price of rice is $x\,\dfrac{\text{dollars}}{\text{gram of rice}}$. We are given that the total price of rice is $4.50\,\text{dollars}$. How can we relate these two quantities with an equation? $\begin{aligned} y\,\text{grams of rice}\cdot x\,\dfrac{\text{dollars}}{\text{gram of rice}}=4.5\,\text{dollars} \end{aligned}$ So in order to find the cost $x$ of rice per gram, we need to figure out the value of $y$, which is the total amount of rice David uses. Notice what other information we are given: $15\,\dfrac{\text{grams of rice}}{\text{gram of spice}}$ $40\,\text{grams of spice}$ $10\,\text{servings}$ $75\,\dfrac{\text{grams of rice}}{\text{serving}}$ Which of these quantities can help us calculate a rate whose units are $\text{grams of rice}$ ? We can combine the following quantities: $\begin{aligned} 10\,\cancel\text{servings}\cdot 75\,\dfrac{\text{grams of rice}}{\cancel\text{serving}}=750\,\text{grams of rice} \end{aligned}$ Now we can plug that in the original equation: $\begin{aligned} 750\,\text{grams of rice}\cdot x\,\dfrac{\text{dollars}}{\text{gram of rice}}&=4.5\,\text{dollars} \\\\ x\,\dfrac{\text{dollars}}{\text{gram of rice}}&=\dfrac{4.5}{750}\,\dfrac{\text{dollars}}{\text{grams of rice}} \\\\ x\,\dfrac{\text{dollars}}{\text{gram of rice}}&=0.006\,\dfrac{\text{dollars}}{\text{gram of rice}} \end{aligned}$ In conclusion, the price of one gram of rice is $0.006$ dollars.